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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 4, Problem 63RE

**(a)**

To determine

**To find: **

The beam of maximal cross sectional area is square.

Expert Solution

The beam of maximal cross sectional area is square.

**Given:**

The radius of the cylinder

**Concept used:**

Pythagoras theorem :- In triangle, the sum of the squares of the lengths of the triangles legs is the same as the square of the length of the triangle hypotenuse.

**Calculation:**

Let

The value of depth and width are equal then area is square.

Form the given data the diagonal of the rectangle length

By using Pythagoras theorem

The area of the rectangule

Now after substituting

**(b)**

To determine

**To find: **

The dimensions of the planks that will have maximal cross-sectional area.

Expert Solution

The dimensions of the planks that will have maximal cross-sectional area is

**Given:**

The radius of the cylinder

**Concept used:**

Pythagoras theorem :- In triangle, the sum of the squares of the lengths of the triangles legs is the same as the square of the length of the triangle hypotenuse.

**Calculation:**

Let

The value of depth and width are equal then area is square.

Form the given data the diagonal of the rectangle length

By using Pythagoras theorem

The area of the rectangule

Now after substituting

Differentiating with respect to

Using the zero product property of the equation

**(c)**

To determine

**To find: **

The dimensions of the strongest beam that cut from the cylindrical log.

Expert Solution

The dimensions of the strongest beam that cut from the cylindrical log is

**Given:**

The radius of the cylinder

**Concept used:**

If the quantities

For some constant

That is y varies inversely proportional as

The constant

**Calculation:**

Let

The value of depth and width are equal then area is square.

Form the given data the diagonal of the rectangle length

By using Pythagoras theorem

The area of the rectangule

Now after substituting

If the quantities

For some constant